Topographic height dependence of internal wave generation by tidal flow over random topography

Internal waves (IWs) generated by tidal flow over the seafloor play a critical role in ocean circulation and climate. We determine the dependence of the radiated IW power on topographic parameters in numerical simulations of tidal flow over two-dimensional random topographic profiles that have the spectrum of oceanic abyssal hills. The IW power increases as the horizontal spatial resolution scale is decreased, but below a certain spatial scale the power saturates at a level less than the linear theory prediction. For increasing topographic RMS height H-rms the emergent interference of the tide and the IWs from different generation sites leads to a transition in the IW power dependence on H-rms from quadratic to linear. This transition in the scaling of the IW power depends on the slopes of a valley's nearest neighboring peaks. Our results should guide the modeling of IW generation by tidal flow over small-scale ocean topography.